On reliability analysis of leader election protocols for virtual traffic lights

This paper addresses the problem of leader election in virtual traffic lights. A virtual traffic light (VTL) is a self-organizing traffic control system that allows road vehicles equipped with vehicle-to-vehicle communication facilities to implement the function of a traffic light without the support of a roadside installation. Previous research has shown that it is impossible to construct a leader election protocol that guarantees agreement among the participating vehicles in the presence of massive communication failures. The paper addresses the problem of calculating the probability of disagreement in situations where a large number of protocol messages are lost due to communication interference, so-called communication grey-outs. To this end, we present a probabilistic analysis of a family of simple round-based consensus algorithms that solve the 1-of-n selection problem. We propose to use these algorithms for the core logic of a VTL leader election protocol (LEP). Our analysis shows that the probability of disagreement depends on: i) the number of vehicles involved in the leader election, ii) the number of rounds of message exchange, iii) the probability of message loss, and iv) the decision criterion used by the LEP. We propose an optimistic and a pessimistic decision criteria for the proposed 1-of-n selection algorithms. The analysis encompass two probabilistic failure models, one for symmetric communication failures and one for asymmetric communication failures.